After reading throw a dice, I decided to look into throwing 2 dice since many games such as monopoly throw 2 dice on each turn.
Using 2 dice makes life more interesting. The most likely throw is 7 - you can never throw 1 and so on. The following code provides some routines for emulating 1 or 2 dice using the simple rand() function.
proc throwdice {} {
set ok 0
while {!$ok} {
set sc [expr 1+int(6*rand())]
if {$sc<7} {set ok 1}
}
return $sc
}
proc throw2dice {} {
lappend all [throwdice]
lappend all [throwdice]
return $all
}
proc throw2dicesum {} {
set thro [ throw2dice]
return [expr [lindex $thro 0]+[lindex $thro 1]]
}
#throwdice emulates a single dice of 6 sides.
#throw2dice returns a list of the results of 2 throwdice;
#throw2dicesum returns the sum of two dice.
proc getfrequency {n} {
# check how often we arrive at each 'square' from 0 with 2 dice thrown to reach square n at least.
set i 0
array set bins {}
set maxbin $n
while {$i<=$maxbin} { set bins($i) 0; incr i}
set i 0
while {$i<40000} { ;# do this number of repeats to get statistical sample.
set j 0
set pos 0
while {$pos<$n} { ;# continue until we reach N
set thro [throw2dicesum]
incr pos $thro
if {$pos<=$n} { ;# if > n then dont count any more.
incr bins($pos)
}
}
incr i
}
puts "Histogram of frequency of reaching square N from origin."
set i 0
while {$i<$maxbin} {
puts "position\t$i\treached\t$bins($i)\ttimes"
incr i
}
histogram [array get bins] 300 250
return 0
}
global ready
set ready 0
proc histogram {slist wid ht} { ;# render a histogram
global ready
array set scores $slist
set nms [lsort -integer [array names scores]]
catch {destroy .h} {}
catch {destroy .b} {}
canvas .h -width $wid -height $ht -bg beige
pack .h
set nbars [array size scores] ;#how many histogram bars
set nax [expr $nbars/10] ;# axis spacing
set hwid [expr $wid/ $nbars]
set i 0
set hmax -9999999 ;# largest y value
set hmin 9999999 ;# smallest y value
while {$i<$nbars} {
set f $scores([lindex $nms $i])
set hmax [ expr {$f>$hmax} ? $f : $hmax]
set hmin [ expr {$f<$hmin} ? $f : $hmin]
incr i
}
if {$hmax>$hmin} {
set i 0
set nay 100
while {$nay<$hmax} {
set yp [expr $ht-0.75*$nay-20]
.h create line 0 $yp $wid $yp -fill red
incr nay 100
}
set nax 10
while {$i<$nbars} {
set x [expr $hwid*$i]
set rhs [expr $x+$hwid/2]
set f [expr $ht-20-.75*$ht*$scores([lindex $nms $i])/$hmax]
.h create rectangle $x [expr $ht-20] $rhs $f -fill gray
if {[expr $i>=$nax]} {
.h create line $x [expr $ht-20] $x 0 -fill red
incr nax 10
}
incr i
incr x $hwid
}
update
button .b -text "Next" -command "incr ready" ;# when ready is changed, proceeds with commands
pack .b
}
}
getfrequency 36Proc getfrequency finds how often you land on each square 0 to n (eg 0-36) no matter how many throws of the dice this takes.
You will find that the number of times your throw lands on a particular square increases, then decreases, and then oscillates a little.
Histogram of frequency of reaching square N from origin. position 0 reached 0 times position 1 reached 0 times position 2 reached 1128 times position 3 reached 2177 times position 4 reached 3385 times position 5 reached 4572 times position 6 reached 5750 times position 7 reached 7411 times position 8 reached 6758 times position 9 reached 6209 times position 10 reached 5826 times position 11 reached 5689 times position 12 reached 5361 times position 13 reached 4964 times position 14 reached 5557 times position 15 reached 5835 times position 16 reached 5880 times position 17 reached 5930 times position 18 reached 5803 times position 19 reached 5784 times position 20 reached 5628 times position 21 reached 5572 times position 22 reached 5710 times position 23 reached 5723 times position 24 reached 5639 times position 25 reached 5782 times position 26 reached 5851 times position 27 reached 5776 times position 28 reached 5593 times position 29 reached 5681 times position 30 reached 5651 times
I used excel to display the graph, but could use the graph plotter.